The most common and most likely answer to this crossword clue is the 4 letter word ANAL
A
N
A
L
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The straight part
We know that "Obsessive" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case obsessive = anal.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does ANAL mean?
ANAL noun- Any of the anal scales of a reptile.
- Anal sex.
- Of, related to, intended for or involving the anus.
- Of the stage in psychosexual development when the child's interest is alleged to be concentrated on the anal region.
- Of a person, compulsive and stubborn, obsessed with neatness and accuracy, supposedly from not having progressed beyond the anal stage.
- (of a vein) Proximate to the thorax.